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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '716883178609633242,743618065688422667', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8363129704525103, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 3]], [5, [1, 0, -1]]], 'bad_primes': [2, 3, 5], 'central_character': '28800.1', 'coefficient_field': '1.1.1.1', 'conductor': 28800, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 0, 3], [1, 0, -1], [1, 0, -2, 0, 49], [1, -8, 38, -88, 121], [1, 4, 30, 52, 169], [1, 0, 30, 0, 289], [1, 0, 22, 0, 361], [1, -8, 62, -184, 529], [1, 0, 54, 0, 841], [1, 0, -2, 0, 961], [1, -12, 110, -444, 1369], [1, 0, 46, 0, 1681], [1, 0, 22, 0, 1849], [1, -8, 110, -376, 2209], [1, 0, 70, 0, 2809], [1, 8, 134, 472, 3481], [1, 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2.4759566740976124, 4.516760267463574, 6.19318007415274, 7.3273354906952495], 'positive_zeros': ['1.23519091396578725398334381678187', '2.60538869357449517223391665121511', '3.26180587408034592610487247010203', '4.28002313553101117805216295070910', '4.61878022728753276110930411726397', '5.70093888866808737514223874839920', '5.99573481729811170443753568761035', '6.97238544391138654785050907555983', '7.00520502565783528594752431201801', '7.88125929411027787932176182764153', '8.635268153066941217007271839151560', '9.022035638415746178025932660186091', '9.401949169928688362704456671527225', '9.851840183892789826086741161767840', '10.65133305239162895186920528545277'], 'prelabel': '4-28800-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1640903135037528, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1460501244298055909, 'z1': {'__RealLiteral__': 0, 'data': '1.23519091396578725398334381678187', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.60538869357449517223391665121511', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.26180587408034592610487247010203', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8363129704525103, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 28800, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 8, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 9, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, -24, 0], 'euler11': [1, -8, 38, -88, 121], 'euler13': [1, 4, 30, 52, 169], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -8, 62, -184, 529], 'euler29': [1, 0, 54, 0, 841], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, -12, 110, -444, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, -8, 110, -376, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, 70, 0, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 12, 182, 876, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 32, 422, 2656, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, 28, 390, 2716, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 3, 0, 0], [1, 0, -1, 0, 0], [1, 0, -2, 0, 49], [1, -8, 38, -88, 121], [1, 4, 30, 52, 169], [1, 0, 30, 0, 289], [1, 0, 22, 0, 361], [1, -8, 62, -184, 529], [1, 0, 54, 0, 841], [1, 0, -2, 0, 961], [1, -12, 110, -444, 1369], [1, 0, 46, 0, 1681], [1, 0, 22, 0, 1849], [1, -8, 110, -376, 2209], [1, 0, 70, 0, 2809], [1, 8, 134, 472, 3481], [1, 4, 126, 244, 3721], [1, 0, 70, 0, 4489], [1, 0, 142, 0, 5041], [1, 12, 182, 876, 5329], [1, 0, 158, 0, 6241], [1, 32, 422, 2656, 6889], [1, 0, 142, 0, 7921], [1, 28, 390, 2716, 9409]], 'index': 2, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.12.1/200.1/a', 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-200.1-a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-28800-1.1-c1e2-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-28800-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1640903135037528, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1460501244298055909, 'z1': {'__RealLiteral__': 0, 'data': '1.23519091396578725398334381678187', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9572409
{'Lhash': '716883178609633242,743618065688422667', 'Lhash_array': ['716883178609633242', '743618065688422667'], 'label': '4-28800-1.1-c1e2-0-2', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-200.1-a'}
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id: 9572158
{'Lhash': '716883178609633242,743618065688422667', 'Lhash_array': ['716883178609633242', '743618065688422667'], 'label': '4-28800-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/200.1/a'}